This study is designed to test the effects of melatonin in two formulations (10mg, 2.5mg time-release) and placebo (no active drug) on the body's temperature regulation and sleep/wake cycle in persons with Alzheimer's disease compared to healthy elderly. People with dementia are frequently awake for long periods during the night, causing fatigue for both the patient and the caregiver. Melatonin may help treat this difficult problem. Melatonin is a hormone produced at night by the pineal gland in the brain. Melatonin may help keep our bodies adjusted to a 24-hour daily rhythm and maintain a normal sleep/wake cycle. We produce less melatonin as we age, so many persons with Alzheimer's Disease make very little of their own. Melatonin may improve sleep when taken in oral capsule form. Melatonin is being studied as an investigational drug, which means the Food and Drug Administration (FDA) has approved its use in this study, but not general use.